Let's do a current path,
current coming from the 2V. battery, flows to R5,
at the same time it flows through R4,
but before it reaches these two, it flows through R3,
but at the same time it flows through R3
it branches through R2, and before it flows through R2
it all starts out flowing through R1.

Let's start with the current path from the 3V. battery, with a short across the 2V. bat.

Lets go to the extreme left side first,

current flows through both R1 and R2 at the same time,
but before that, it has to flow through R3 to get there,
however as it is approaching R3, at the same time part of it is branching off and flowing through R5,
But before any of this can happen it has to flow through R4 to begin the whole process.